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Last modified on August 3rd, 2023

The surface area, or total surface area (TSA), of a hexagonal pyramid, is the entire space occupied by its seven faces. It is measured in square units such as m^{2}, cm^{2}, mm^{2}, and in^{2}.

The formula is given below:

The formula to calculate the surface area of a hexagonal pyramid also includes its lateral surface area (LSA).

**Lateral Surface Area ( LSA)**

∴ **Total Surface Area ( TSA) = 3ab + LSA**

Let us solve some examples to understand the concept better.

**Find the lateral and total surface areas of a hexagonal pyramid with a base of 5 cm, an apothem of 4.33 cm, and a slant height of 9 cm.**

Solution:

As we know,

Lateral Surface Area (*LSA*) = 3bs, here b = 5 cm, s = 9 cm

∴ *LSA* = 3 × 5 × 9

= 135 cm^{2}

Total Surface Area (*TSA*) = 3ab + *LSA,* here a = 4.33 cm, b = 5 cm, *LSA *= 135 cm^{2}

∴*TSA* = 3 × 4.33 × 5 + 135

= 199.95 cm^{2}

Finding the surface area of a hexagonal pyramid when the **BASE** and **HEIGHT** are known

**Find the surface area of a hexagonal pyramid with a base of 4 cm, and a height of 6 cm.**

Solution:

We will use an alternative formula for finding the surface area of a hexagonal pyramid.

Total Surface Area (*TSA*) = ${\dfrac{3\sqrt{3}}{2}b^{2}+3b\sqrt{h^{2}+\dfrac{3b^{2}}{4}}}$, here b = 4 cm, h = 6 cm

∴ *TSA* = ${\dfrac{3\sqrt{3}}{2}\times 4^{2}+3\times 4\times \sqrt{6^{2}+\dfrac{3\times 4^{2}}{4}}}$

= 124.71 cm^{2}

Last modified on August 3rd, 2023

When exactly does the alternative formula work?

It works as the basic formula cannot be applied here.

We use the alternative formula to calculate the surface area of a hexagonal pyramid when the base and height are known.